We use a pseudodifferential calculus on differentiable groupoids to obtain new analytical results on geometric operators on certain noncompact Riemannian manifolds. The first step is to establish that the geometric operators belong to a pseudodifferential calculus on an associated differentiable groupoid. This then leads to Fredholmness criteria for geometric operators on suitable noncompact manifolds, as well as to an inductive procedure to compute their essential spectra. As an application, we answer a question of Melrose on the essential spectrum of the Laplace operator on manifolds with multicylindrical ends.
|Original language||English (US)|
|Number of pages||9|
|Journal||Electronic Research Announcements of the American Mathematical Society|
|State||Published - May 8 2001|
All Science Journal Classification (ASJC) codes